Non-uniform time sampling for multiple-frequency harmonic balance computations

A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows. It has recently received significant attention, especially in t...

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Bibliographic Details
Published in:Journal of computational physics 2013-03, Vol.236, p.317-345
Main Authors: Guédeney, Thomas, Gomar, Adrien, Gallard, François, Sicot, Frédéric, Dufour, Guillaume, Puigt, Guillaume
Format: Article
Language:English
Subjects:
Almost-periodic flow
Computation
Condition number
Fourier analysis
Harmonic balance
Harmonic balance method
Outlets
Robustness
Sampling
Stability
Time marching
Time sampling
Turbomachinery
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Summary:A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows. It has recently received significant attention, especially in the turbomachinery field where the flow spectrum is essentially a combination of the blade passing frequencies. Up to now, harmonic balance methods have used a uniform time sampling of the period of interest, but in the case of several frequencies, non-necessarily multiple of each other, harmonic balance methods can face stability issues due to a bad condition number of the Fourier operator. Two algorithms are derived to find a non-uniform time sampling in order to minimize this condition number. Their behavior is studied on a wide range of frequencies, and a model problem of a 1D flow with pulsating outlet pressure, which enables to prove their efficiency. Finally, the flow in a multi-stage axial compressor is analyzed with different frequency sets. It demonstrates the stability and robustness of the present non-uniform harmonic balance method regardless of the frequency set.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2012.11.010